The present invention relates to a method and apparatus for measuring physical properties of a sample of matter, including the mass, volume, density, and bulk modulus. More particularly, the invention relates to a method and apparatus which automatically measures a buoyancy force versus gas density relationship.
The density of a substance is expressed as a ratio of mass m to volume V, or m/V. This is a physical property of a material which relates to composition, level of impurities, and mixtures, and can be an indicator of hidden features such as voids. In the case of compressible media, such as closed-pore solids, the bulk density is a function of hydrostatic pressure, since the volume changes but the mass remains constant.
There exist two popular methods for determining the density of a solid: (1) by comparison of the sample density with the densities of substances of known value, usually by hydrostatic weighing in two different fluids of known and substantially different density (Archimedes principle), and (2) by the independent measurement of mass and volume of the sample.
Considering the first method, the weight of an object is measured in two liquids having significantly different densities. The measured weight, also referred to herein as apparent weight, is reduced from the true weight due to buoyancy forces acting on the object. Thus, the apparent weight is the true weight minus the buoyancy force, where the buoyancy force is equal to the weight of the liquid displaced by the object. When in the higher density liquid, the buoyancy force acting on the object is greater, and the apparent weight of the object is less. The sensitivity of the method ultimately relies on the range in available liquid densities. In one method of using hydrostatic weighing techniques, one measures the apparent weight of an object in alcohol and then in water, where the alcohol and the water have densities of 0.791 and 1.0 g/cc, respectively. It is also common practice to weigh the object in air and then in water or alcohol, thus using air as the first medium. In that case it is common practice to assume the weight in air to be the xe2x80x9ctrue weightxe2x80x9d of the object. The specific reasons for using a liquid as one of the mediums in this technique are (i) to obtain a large difference in density between the two fluids, and (ii) to increase the effect of buoyancy forces.
For very accurate measurement of density, there are several experimental problems which are typically ascribed to the hydrostatic weighing method using two liquids. First, the method suffers from the necessity of weighing an object in liquid. Strictly as a practical matter, this requires suspending the object via a tether or thin wire in the liquids. Second, related to the first, is the fact that surface tension forces affect the measurement as the liquid meniscus either pulls the tether down into the liquid or pushes it up into the adjacent gas (typically air), depending on whether the liquid wets the tether easily. Third, the density of the liquid is affected by dissolved gases in the liquid. Since the effect of trapped gas is to change the actual density of the liquid, efforts must be made to eliminate the trapped gas. Fourth, results will vary due to bubbles of trapped gas on irregular sample surfaces of the object. The bubbles that cling due to surface tension displace liquid and affect the measured buoyancy forces.
The second common approach to determine density requires independent determination of both the mass and the volume. One measures the mass of the body using conventional state-of-the-art balances common to most laboratories. Commercial devices exist for performing this step to very high precision and accuracy. The volume is determined independently. If the sample is of a uniform geometry, it may be possible to calculate the specimen volume based on measurable dimensions. In the more general case where samples are of irregular shape, the volume is determined by a method commonly referred to as pycnometry. For reasonably sized samples on the order of 0.5 cubic centimeters and larger, commercial pycnometers are available for determining volume to 0.02%. Pycnometers typically consist of two chambers connected by means of a pathway for a gas to move and a valve which can isolate the two chambers. The exact volume of one of the chambers must be known apriori. The second chamber is of arbitrary, but similar size. The first chamber, of known volume, is pressurized using a gas such as helium to a predetermined pressure. The second chamber is initially empty and is evacuated by means of a vacuum pump. By means of valves, the two chambers are then isolated from the gas source and from the vacuum pump leaving the first chamber at an elevated pressure with helium and the second chamber under vacuum. The valve in the passageway connecting the two chambers is then opened and the pressurized gas is allowed to expand from the first chamber into the second chamber, and the pressure achieves a new equilibrium value by virtue of the increased volume occupied by the gas. It is a straightforward calculation to determine the volume of the unknown chamber using the initial helium pressure in the first chamber, the volume of the first chamber, and the final pressure. The steps are then repeated with the sample of interest being placed into the second chamber. The newly calculated volume of the second chamber represents the remaining volume of the second chamber not occupied by the sample.
Although the field of pycnometry is well established for accurately determining the volumes of solids of reasonable sizes, the state-of-the-art is limited by several factors in attempts to extrapolate to smaller samples. There are many industries where large samples are not always available. Some specific applications would include high-temperature superconducting wires, samples pertaining to the study of irradiation, and porous membranes used for delivering and mixing gases, such as in the fuel cell applications. The volume of such samples is often much smaller than that required by pycnometers. For accurate measurements, the sample should occupy a significant fraction of the chamber volume, e.g. 50-60% of a 1 cubic centimeter chamber.
There are several other limitations to the pycnometry method for determining density. First, if safeguards are not included, temperature variations of the gas due to room temperature fluctuations may affect the pressure, and hence the density, of the pressurized gas. Second, the gas-comparison pycnometer described above does not work if there are any leaks in the system. The ability of the technique to work depends strongly upon the number of gas atoms remaining constant before and after the gas expands into the second chamber. Third, the chamber door, when closed, must close in a repeatable fashion such that the volume of the chamber is exactly the same every time the door is opened and closed. Fourth, the mechanism requires a vacuum pump. Fifth, the true volume of the pressurized chamber must be known to better tolerances than the desired accuracy of sample volume. Finally, the mass must be measured by a separate device.
Thus, there are significant limitations associated with the prior art. The current invention offers significant improvements over the prior art, as will become apparent in the following description of invention.
The foregoing and other needs are met by an apparatus for determining density of a sample having a sample mass and a sample volume while the sample is immersed in a gaseous medium having variable density. According to the invention, the sample is exposed to an acceleration in a first direction and a net buoyancy force in a second direction opposite the first direction, where the net buoyancy force is the sum of buoyancy forces in the first and second directions exerted on the sample by the gaseous medium. The apparatus includes a chamber for containing the gaseous medium and the sample immersed in the gaseous medium, and means for selectively varying the density of the gaseous medium in the chamber over a range of densities. The apparatus also includes means for producing at least one electrical signal related to the density of the gaseous medium in the chamber as the density of the gaseous medium is varied.
A balance beam, having opposing first and second ends, is disposed within the chamber. The balance beam includes a sample pan disposed adjacent the first end of the balance beam. The sample pan has a sample pan volume and a sample pan mass, and creates a sample pan moment adjacent the first end of the balance beam. Disposed adjacent the second end of the balance beam is a first counter-weight having a first counter-weight volume which is substantially equivalent to the sample pan volume, a first counter-weight mass which is substantially equivalent to the sample pan mass, and which creates a first counter-weight moment that is substantially equivalent to the sample pan moment. Disposed adjacent the second end of the balance beam is a coil assembly having a coil assembly volume and a coil assembly mass, and which creates a coil assembly moment adjacent the second end of the balance beam. A second counter-weight is disposed adjacent the first end of the balance beam. The second counter-weight has a second counter-weight volume which is substantially equivalent to the coil assembly volume, a second counter-weight mass which is substantially equivalent to the coil assembly mass, and creates a second counter-weight moment which is substantially equivalent to the coil assembly moment.
The apparatus also includes a magnet assembly disposed adjacent to and magnetically interacting with the coil assembly. A controller provides a coil current to the coil assembly, thereby generating a magnetic field which interacts with the magnet assembly. According to the invention, the interaction between the magnetic field of the coil assembly and the magnet assembly causes a force to be applied to the second end of the beam to keep the beam balanced as the density of the gaseous medium in the chamber is varied over the range of densities. The force applied to the second end of the beam is substantially equivalent to the difference between the net buoyancy force and the product of the sample mass times the acceleration while the sample is immersed in the gaseous medium as the density of the gaseous medium is varied over the range of densities. A computing device receives the electrical signal related to the density of the gaseous medium and the electrical signal related to the coil current, and calculates the density of the sample based thereon.
In another aspect, the invention provides a method for determining density of an object. The method includes completely immersing the object in a gaseous medium, causing the gaseous medium to have a first density, and determining the first density of the gaseous medium. While immersed in the gaseous medium having the first density, the object is exposed to an acceleration in a first direction. The method includes determining a first applied force in a second direction opposite the first direction, where the first applied force is sufficient to maintain the object in static equilibrium while the acceleration. The method further includes causing the gaseous medium to have a second density which differs from the first density by at least about 0.015 grams per cubic centimeter, determining the second density of the gaseous medium, and exposing the object to the acceleration in the first direction while immersed in the gaseous medium having the second density. A second applied force in the second direction is determined which is sufficient to maintain the object in static equilibrium while exposed to the acceleration and immersed in the gaseous medium having the second density. Based on the first and second densities of the gaseous medium and the first and second applied forces, the density of the object is determined to an uncertainty of no greater than about 0.6 percent.
Preferred embodiments of the method include steps of completely immersing a calibration standard of known density in the gaseous medium having the first density, and exposing the calibration standard to the acceleration in a first direction while immersed in the gaseous medium having the first density. While the acceleration is applied and the calibration standard is immersed in the gaseous medium having the first density, a third applied force in the second direction is determined, where the third applied force is sufficient to maintain the calibration standard in static equilibrium. The method includes causing the gaseous medium to have the second density, and exposing the calibration standard to the acceleration in the first direction while immersed in the gaseous medium having the second density. A fourth applied force in the second direction is determined which is sufficient to maintain the calibration standard in static equilibrium while exposed to the acceleration and immersed in the gaseous medium having the second density. Based on the third and fourth applied forces, the first and second densities of the gaseous medium, and the known density of the calibration standard a calibration ratio is calculated. The density of the object is then determined based on the first and second densities of the gaseous medium, the first and second applied forces, and the calibration ratio.
In some preferred embodiments, the calibration ratio is determined according to:                     C        1            /              C        2              =                            V          a4                ⁡                  (                                    ρ              C                        -                          ρ              1                                )                                      V          a3                ⁡                  (                                    ρ              C                        -                          ρ              2                                )                      ,
where C1/C2 is the calibration ratio, xcfx81c is the density of the calibration standard, xcfx811 is the first density of the gaseous medium, xcfx812 is the second density of the gaseous medium, Va3 is a voltage related to the third applied force, and Va4 is a voltage related to the fourth applied force. The density of the object is then determined according to:             ρ      o        =                                                      V              a1                        ⁡                          (                                                C                  1                                /                                  C                  2                                            )                                ⁢                      ρ            2                          -                              V            a2                    ⁢                      ρ            1                                                            V            a1                    ⁡                      (                                          C                1                            /                              C                2                                      )                          -                  V          a2                      ,
where xcfx810 is the density of the object, Va1 is a voltage related to the first applied force, and Va2 is a voltage related to the second applied force.